Class vec

Overview

Class vec implements in an object-oriented fashion two-dimensional euclidean vectors of double, offering operators for all its elementary operations.

Nested service classes are provided in order to deal properly with the 2D toroidal space of the simulation.

Interface

Constructors

• vec()

  builds a vector with uninitialized components.

• vec(const double &, const double &)

  builds a vector with the two given components.

• vec(int)

  given a fold variable (see below for nested enum fold), builds a vector that represents the corresponding fold, represented by the integer.

Methods

• vec normalize() const

  returns the vector normalized.

Operators

• vec operator - () const

  returns the reverse of the vector.

• vec operator + (const vec &) const

  returns the sum of the two vectors.

• vec & operator += (const vec &)

  sums the right hand operand to the left hand operand.

• vec operator - (const vec &) const

  returns the difference of the two vectors.

• vec & operator -= (const vec &)

  subtracts the right hand operand to the left hand operand.

• vec operator * (const double &) const

  returns the vector multiplied by the scalar. (A corresponding external operator vec operator * (const double &, const vec &) is provided)

• vec & operator *= (const double &)

  multiplies the vector for the given double.

• vec operator / (const double &) const

  returns the vector quotient.

• vec & operator =/ (const double &)

  divide the vector for the given double.

• vec operator % (const double &) const

  returns the vector rotated for a given amount of radiants.

• vec & operator %= (const double &)

  rotates the vector for a given amount of radians.

• double operator ^ (const vec &) const

  returns the cross product.

• double operator * (const vec &) const

  returns the scalar product.

• double operator ~ () const

  returns the squared module.

• double operator ! () const

  returns the module.

• bool operator == (const vec &) const

  equality operator.

• std :: ostream & operator << (std :: ostream &, const vec &)

  standard output.

Nested enum fold

Overview

Enum fold is a bitmask-wise object for representing the possible combination of translations inside the toroidal space of the simulation. It’s made of six elements:

• 2 horizontal translations left, right
• 2 vertical translations up, down
• 1 null translation direct
• 2 bitmask-wise extracting elements horizontal, vertical

It’s possible to assemble one horizontal and one vertical translation into a single integer representation with the operator ||. It’s also possible to check the horizontal or the vertical component of the integer representation with one extraction element and the operator &&.

REMARK: the simulation always works within a range ([0,1],[0,1]).

Declaration

enum fold {direct = 0x0, left = 0x1, right = 0x2, up = 0x4, down = 0x8, horizontal = 0x3, vertical = 0xc};

Example usage of fold

int horizontal_fold = vec :: left;
int vertical_fold = vec :: up;
int my_fold = vec :: down || vec :: right;
int no_fold = vec :: direct;

std :: cout << vec(horizontal_fold) << std :: endl; \\ Prints (-1, 0)
std :: cout << vec(vertical_fold) << std :: endl; \\ Prints (0, 1)
std :: cout << vec(my_fold) << std :: endl; \\ Prints (1, -1)
std :: cout << vec(no_fold) << std :: endl; \\ Prints (0, 0)
std :: cout << vec(my_fold && vec :: vertical) << std :: endl; \\ Prints (0, -1)